In 1950 Cockell entered a brief tournament to crown a new British light-heavyweight champion, recently vacated due to the retirement of Freddie Mills.

Cockell defeated Jimmy Carroll in an eliminator match (avenging a previous loss to him in the process) before facing Mark Hart on 17 October at Harringay Arena.

[1] Cockell fought and won two more fights against future Hall of Famer Lloyd Marshal, before challenging the Frenchman Albert Yvel for his European light-heavyweight title.

The bout took place on 27 March 1951 at Earls Court, London, and Cockell won the title by scoring a technical knockout in the sixth round.

Cockell then fought against Randolph Turpin, who the year before, had become one of the few to defeat Sugar Ray Robinson, becoming world middleweight champion as a result before losing his title in the rematch.

The third one was against the Welshman, Tommy Farr, who had been an excellent heavyweight, fighting against the great Joe Louis, but who was now at the end of his career, and although experienced, had aged quite a bit.

The bout for the British and Commonwealth titles was held at Harringay Arena on 12 May 1953, and Cockell won on points over fifteen rounds.

In covering the fight for Sports Illustrated, Budd Schulberg wrote in the 30 May 1955 edition, "Except for the technicality of wearing eight-ounce gloves, Don Cockell's stand against Rocky Marciano in the fading daylight hours of a cool San Francisco sunlit day was a glorious—or appalling—throwback to this pre-Marquess of Queensberry condition.

This was a bare-knuckle brawl with gloves—and not a pleasant sight either—as an uncouth, merciless, uncontrolled and truly vicious fighter (the unbeaten Champion Marciano) wore down an ox-legged, resolute fat man who came into the ring with the honor of the British Empire weighing heavily—and consciously—on his massive, blubbery shoulders.

He had promised his Union Jack supporters that he would not let them down, and the first words he mumbled through swollen lips after his fearful beating in nine rounds were an apology to his fellow countrymen for not having done better."

Jack Gallagher of the Oakland Tribune praised Cockell's brave effort, writing, "The fight was all Rocky's from the beginning.

In September 1955 he lost to the Cuban contender Nino Valdes at the White City Stadium by a technical knockout in the third round.

By 1975 he was working as a craftsman blacksmith in the permanent way machine shops at the London Underground Lillie Bridge Depot in Fulham.